1. ## Integrals

find the following indefinite integral (using u substitution):

$\displaystyle \int x \sqrt[3]{x+1} dx$

evaluate the following definite integrals using the Fundamental Theorem of the Calculus (u sub involved):

$\displaystyle \int_{0}^{\frac{\pi}{4}} (1 + tan^2 x)sec^2 x dx$

$\displaystyle \int_{0}^{2|b|} \frac{x}{\sqrt{x^2 + b^2}} dx$

2. Originally Posted by qzno
find the following indefinite integral (using u substitution):

$\displaystyle \int x \sqrt[3]{x+1} dx$

evaluate the following definite integrals using the Fundamental Theorem of the Calculus (u sub involved):

$\displaystyle \int_{0}^{\frac{\pi}{4}} (1 + tan^2 x)sec^2 x dx$

$\displaystyle \int_{0}^{2|b|} \frac{x}{\sqrt{x^2 + b^2}} dx$
1) Let $\displaystyle u=x+1$

2) Let $\displaystyle u=\tan x$

3) Let $\displaystyle u=x^2+b^2$

3. I already tried this for them all haha

4. for the second one I got the evaluated answer to be:

$\displaystyle \frac{(tan 1)^3}{3}$

is this correct?

and i still cant do the last question : (
thanks to anyone who helps!!

5. For the first one when i let u = x + 1, i got the answer to be: $\displaystyle \frac{3x(x+1)^{\frac{4}{3}}}{4} + c$
is this correct?

i still havnt figured out the third one : (